New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rmo3 Unicode version

Theorem rmo3 3133
 Description: Restricted "at most one" using explicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmo2.1
Assertion
Ref Expression
rmo3
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem rmo3
StepHypRef Expression
1 df-rmo 2622 . 2
2 sban 2069 . . . . . . . . . . 11
3 clelsb3 2455 . . . . . . . . . . . 12
43anbi1i 676 . . . . . . . . . . 11
52, 4bitri 240 . . . . . . . . . 10
65anbi2i 675 . . . . . . . . 9
7 an4 797 . . . . . . . . 9
8 ancom 437 . . . . . . . . . 10
98anbi1i 676 . . . . . . . . 9
106, 7, 93bitri 262 . . . . . . . 8
1110imbi1i 315 . . . . . . 7
12 impexp 433 . . . . . . 7
13 impexp 433 . . . . . . 7
1411, 12, 133bitri 262 . . . . . 6
1514albii 1566 . . . . 5
16 df-ral 2619 . . . . 5
17 r19.21v 2701 . . . . 5
1815, 16, 173bitr2i 264 . . . 4
1918albii 1566 . . 3
20 nfv 1619 . . . . 5
21 rmo2.1 . . . . 5
2220, 21nfan 1824 . . . 4
2322mo3 2235 . . 3
24 df-ral 2619 . . 3
2519, 23, 243bitr4i 268 . 2
261, 25bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wnf 1544  wsb 1648   wcel 1710  wmo 2205  wral 2614  wrmo 2617 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-cleq 2346  df-clel 2349  df-ral 2619  df-rmo 2622 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator